Spectral Curves and Localization in Random Non-Hermitian Tridiagonal Matrices

Details Spectral Curves and Localization in Random Non-Hermitian Tridiagonal Matrices Spectral Curves and Localization in Random Non-Hermitian Tridiagonal Matrices

2009-05-15

arxiv.org/abs/0905.2489v2

J. Phys. A: Math. Theor. 42 (2009) 395204 (9pp.)

Physics

Mathematical Physics

5 pages, 9 figures, typographical error corrected in references

Scientific paper

10.1088/1751-8113/42/39/395204

Eigenvalues and eigenvectors of non-Hermitian tridiagonal periodic random matrices are studied by means of the Hatano-Nelson deformation. The deformed spectrum is annular-shaped, with inner radius measured by the complex Thouless formula. The inner bounding circle and the annular halo are stuctures that correspond to the two-arc and wings observed by Hatano and Nelson in deformed Hermitian models, and are explained in terms of localization of eigenstates via a spectral duality and the Argument principle.

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